$A$ $B$ $C$ If: $ AB = 2x + 6$, $ AC = 51$, and $ BC = 6x + 5$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 6} + {6x + 5} = {51}$ Combine like terms: $ 8x + 11 = {51}$ Subtract $11$ from both sides: $ 8x = 40$ Divide both sides by $8$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 6({5}) + 5$ Simplify: $ {BC = 30 + 5}$ Simplify to find ${BC}$ : $ {BC = 35}$